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Quantum communication links and networks are needed for secure information exchange and for interconnecting future quantum computers. However, their capacity decreases exponentially with distance due to the effect of fiber attenuation that cannot be undone by amplification (although quantum repeaters are an active area of research, they are almost as hard to build as quantum computers). Hence, the only way to increase the quantum communication capacity is by employing more degrees of freedom (optical modes) over which this information can be encoded and transmitted. While frequency (WDM), temporal, and polarization modes have already been exploited for this purpose, the use of many spatial modes has only recently become possible owing to the development of low-loss few-mode fibers (FMFs). This talk will present the work of Prof. M. Vasilyev’s research group on the development of two key enablers of quantum communication over spatial modes of FMFs: 1) generator of spatially-entangled photon pairs and 2) receiver sub-system that can perform projective measurements that alternate between two sets of mutually unbiased bases in a given spatial mode space (this sub-system can also perform dynamically reconfigurable de-multiplexing of spatial modes of the FMF). Both of the above devices / sub-systems are based on the spatial-mode-selective quantum frequency conversion process, implemented in a medium with either second-order nonlinearity (multimode lithium niobate waveguide) or third-order nonlinearity (custom-made FMF). The talk will introduce the principles of their operation, as well as the recent experimental results obtained in both media.